I have a 436HP and I am having the same issue with it too... They say the internal time/clock batteries run low and lose thier charge. Uniden suggests to leave your unit plugged in for 48hrs+ to recharge the internal battery. It's best to turn the radio off while doing this.
If this does not work then your internal time/clock battery is in need of service and to contact Uniden support. There is a repair campaign for the BCD436HP units and will replace it for free. Not sure about other models?
Most of the early production x36HP models had RTC problems. Uniden redesigned the RTC circuit which is replaced under the repair campaign in the 4 and 536HP models. I'm pretty sure the new design now uses a super capacitor instead of a tiny rechargeable lithium cell. The super caps still need to be charged by powering them externally like you said. I think the 436 charged the RTC cell while on or off and the 536 needed to be powered on for 50+ hours. That was with the original Lithium cells. I have no idea if repaired or new models that use a super cap need the 40 or 50 hour charge time. The super caps may charge up much quicker.
I thought I read that the HP-2 also uses a super cap instead of a lithium cell while the older HP-1's still used a lithium cell for the RTC backup.
Super caps can go bad over time but generally they are pretty reliable.
I'm also not sure if Uniden released a firmware for the HP-1 or 2 that gave the set clock warning a default timeout where the radio would start scanning even if you did not set the time. They did that for the x36HP models so they would go into scan even if the clock was not set. I think it took somewhere around 5 to 10 seconds before it would timeout and go into scan.
They did the same for the Serial or Mass Storage mode screen also. They used to hang on that screen waiting for user input but Uniden created a firmware the let the scanner select serial port mode if the user did not enter a choice. I'm also not sure if this was carried over to the HP-1 or 2 either.
